2007/09/28 by Philippe Michel, Dinakar Ramakrishnan, Michel, Philippe +1 · 2 citations
Mathematics · #11F11 #11F12 #11F67 #FOS: Mathematics #Functional Equations Stability Results #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT #msc:11F11 #msc:11F12 #msc:11F67
paper · pdf · doi:10.48550/arxiv.0709.4668
arxiv created 2007/09/28 · openalex publication_date 2007/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate some consequences of the Gross/Zagier types of formulae which were introduced by Gross and Zagier, and were then generalized in various directions by Hatcher, Zhang, Kudla and several other people. Working in the classical context of central values of L-series of holomorphic forms of prime level, we deduce an exact average formula for suitable twists of such L-values, with a relation to the class number of associated imaginary quadratic fieds, thereby strengthening a result of Duke. One also obtains a stability result, as well as subconvexity (in this setting), and certian non-vanishing assertions. This article is dedicated to the memory of Serge Lang.